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A right circular cone is inscribed inside a larger right circular cone with a volume of 100 cms. The axes of the cones coincide, and

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A right circular cone is inscribed inside a larger right circular cone with a volume of 100 cms. The axes of the cones coincide, and the vertex of the inner cone touches the center of the base of the outer cone. Find the ratio of the heights of the cones that maximizes the volume of the inner cone. The ratio of the height of the inner cone to the height of the outer cone is

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